<html>
 <head>
  <meta charset="UTF-8">
 </head>
 <body>
  <p data-lake-id="u2b4daa22" id="u2b4daa22"><br></p>
  <h1 data-lake-id="f2nZA" id="f2nZA"><span data-lake-id="u7fc83573" id="u7fc83573">典型回答<br><br></span></h1>
  <p data-lake-id="ud3f4ab06" id="ud3f4ab06"><span data-lake-id="u152f93e2" id="u152f93e2">"直到生出男孩为止"说明了：</span></p>
  <p data-lake-id="u30c347f9" id="u30c347f9"><span data-lake-id="u348b4326" id="u348b4326"> (1) 每家生了男孩后便不再生了 </span></p>
  <p data-lake-id="u7b2e4bee" id="u7b2e4bee"><span data-lake-id="u3750ed5c" id="u3750ed5c"> (2) 每家都只有一个男孩 </span></p>
  <p data-lake-id="ubc8d75a3" id="ubc8d75a3"><span data-lake-id="u9131ba6f" id="u9131ba6f">​</span><br></p>
  <p data-lake-id="u33a30c31" id="u33a30c31"><span data-lake-id="u33490643" id="u33490643"> 那么我们可以先求出每家孩子个数的期望设为X </span></p>
  <p data-lake-id="ud90e67fd" id="ud90e67fd"><span data-lake-id="uba4d9eda" id="uba4d9eda"> X P(概率) </span></p>
  <p data-lake-id="u04d8bf25" id="u04d8bf25"><span data-lake-id="udf1f859d" id="udf1f859d"> 1 0.5 //第一次就生出了男孩的概率是0.5 </span></p>
  <p data-lake-id="u791cbe8a" id="u791cbe8a"><span data-lake-id="u246369ce" id="u246369ce"> 2 0.5^2 </span></p>
  <p data-lake-id="u8e947b85" id="u8e947b85"><span data-lake-id="uc28350b6" id="uc28350b6"> ... </span></p>
  <p data-lake-id="u07a5b9e2" id="u07a5b9e2"><span data-lake-id="u5687c4fa" id="u5687c4fa"> E(X) = </span><span data-lake-id="uc9d2aaad" id="uc9d2aaad">1*0.5+ 2*0.5^2+...= 1/0.5=2</span></p>
  <p data-lake-id="u904e3909" id="u904e3909"><span data-lake-id="u493b63c8" id="u493b63c8">​</span><br></p>
  <p data-lake-id="ud49f0a1a" id="ud49f0a1a"><span data-lake-id="u3859b152" id="u3859b152">每家孩子个数的期望是2，而且都有且只有1个男孩，那么女孩的个数也是1</span></p>
  <p data-lake-id="ue0ef6f13" id="ue0ef6f13"><span data-lake-id="u2566be19" id="u2566be19">​</span><br></p>
  <p data-lake-id="u5292b137" id="u5292b137"><span data-lake-id="u814b4018" id="u814b4018">所以男孩和女孩个数相等！</span></p>
 </body>
</html>